Recurrence flow measure of nonlinear dependence
非线性依赖的复现流度量AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要明确研究多时间序列的非线性滞后依赖及时间延迟嵌入方法。
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非线性依赖的复现流度量
- 研究问题
- 如何度量多个时间序列之间具有不同时间尺度的非线性滞后依赖，并据此为吸引子重构选择合适的非均匀嵌入延迟？
- 方法与思路
- 作者利用复现图中反映可预测动态的对角线形成结构，构造复现流依赖度量，并以确定性系统的时间延迟变量展示用途。
- 材料陈述的贡献
- 摘要称给定复现图后，该度量计算无需额外参数，可捕捉多时间尺度滞后相关，并帮助识别非均匀延迟。
- 阅读关注点
- 读全文时应核对复现图本身的构造参数、依赖度量定义、延迟选择规则，以及面对观测噪声与有限样本时的表现。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或获期刊接收；无参数描述限于给定复现图之后，摘要未提供统计推断保证。
原文摘要
Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. By using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence based state space reconstruction algorithm.